Advertisements
Advertisements
प्रश्न
If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`
Advertisements
उत्तर
In the given problem, we have to find the value of `x^3 + 1/x^3.`
Given: `x^4 + 1/x^4 = 194`
We know that,
`(x^2 + 1/x^2)^2 = x^4 + 1/x^4 + 2` ...[Using (a + b)2 = a2 + b2 + 2ab]
Now, substituting the given value
`(x^2 + 1/x^2)^2 = 194 + 2`
∴ `(x^2 + 1/x^2)^2 = 196`
∴ `x^2 + 1/x^2 = sqrt196`
∴ `x^2 + 1/x^2 = +-14`
Let’s relate it to `x^3 + 1/x^3`
`(x + 1/x)^2 = x^2 + 1/x^2 + 2` ...[Using (a + b)2 = a2 + b2 + 2ab]
`(x + 1/x)^2 = 14 + 2`
∴ `x + 1/x = sqrt16`
∴ `x + 1/x = +-sqrt4`
Thus,
`x^3 + 1/x^3 = (x + 1/x)^3 - 3(x + 1/x)`
`x^3 + 1/x^3 = (4)^3 - 3(4)`
`x^3 + 1/x^3 = 64 - 12`
∴ `x^3 + 1/x^3 = +-52`
संबंधित प्रश्न
Factorise the following using appropriate identity:
4y2 – 4y + 1
Factorise the following using appropriate identity:
`x^2 - y^2/100`
Write the following cube in expanded form:
(2a – 3b)3
Evaluate the following using suitable identity:
(99)3
Factorise the following:
27 – 125a3 – 135a + 225a2
Evaluate following using identities:
(a - 0.1) (a + 0.1)
Evaluate the following using identities:
117 x 83
Evaluate the following using identities:
(0.98)2
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
Write in the expanded form (a2 + b2 + c2 )2
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
Find the cube of the following binomials expression :
\[4 - \frac{1}{3x}\]
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
Use identities to evaluate : (502)2
Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Evaluate: `(2"a"+1/"2a")(2"a"-1/"2a")`
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Expand the following:
(a + 3b)2
Expand the following:
(x - 3y - 2z)2
Evaluate the following without multiplying:
(999)2
Evaluate the following without multiplying:
(1005)2
If m - n = 0.9 and mn = 0.36, find:
m + n
If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 + c2.
Expand the following:
(3a – 2b)3
Find the following product:
`(x/2 + 2y)(x^2/4 - xy + 4y^2)`
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
